Mathematical Sciences: Residual Intersections and Linkage ofCohen-Macaulay Ideals

点击翻译按钮获取中文摘要

This research is in the general area of commutative algebra. The project is concerned with the question of which ring theoretic properties are preserved under residual intersections. In addition, the principal investigator will find necessary and sufficient conditions for an ideal to be in the linkage class of a complete interesection. One goal in the study of commutative rings is to classify ideals having certain properties. Many of these results have applications to problems and counterparts in algebraic geometry. One interesting topic is whether an ideal related by linkage to another ideal shares any of the second ideals interesting properties, or to what extent it does so. This latter problem is the primary concern of this project.